This paper is concerned with chaos in a delay difference equation. The map of the system is proved to be chaotic in the sense of both Devaney and Li-Yorke under some conditions, by employing the snap-back repeller theory. Some computer simulations are provided to illustrate the theoretical result.
{"title":"Chaotic Behavior in a Delay Difference Equation","authors":"Zongchen Li, Di Liang, Qingli Zhao","doi":"10.1109/IWCFTA.2012.23","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.23","url":null,"abstract":"This paper is concerned with chaos in a delay difference equation. The map of the system is proved to be chaotic in the sense of both Devaney and Li-Yorke under some conditions, by employing the snap-back repeller theory. Some computer simulations are provided to illustrate the theoretical result.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"199 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114875801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The simplified quasi-cubics function is used quite common in the ordinary differential equation, which is used to describe the biological neuron model. As complexity of the biological neuron model, its analytical solution hardly can be solved in common situation. Numerical solution of the model is very important in reality. Three fast convergence methods are proposed for the simplified function by means of changing the step size of the classical Euler method in this manuscript. The results obtained are pretty good. First method is to correct the step size of two directions. Second method is to correct and encrypt two directions' step size. And the last method is to search unidirectional step size. On one hand, the feasibility of the three methods are proved based on the theoretical analysis. On the other hand, numerical results and comparison show that the advised three methods are effective to get the numerical solution with small population size, enhanced convergence speedup and improved precision.
{"title":"Three Improved Euler Methods for a Class of Simplified Quasi-cubics Function","authors":"Ya Wang, Yongguang Yu, Sha Wang","doi":"10.1109/IWCFTA.2012.29","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.29","url":null,"abstract":"The simplified quasi-cubics function is used quite common in the ordinary differential equation, which is used to describe the biological neuron model. As complexity of the biological neuron model, its analytical solution hardly can be solved in common situation. Numerical solution of the model is very important in reality. Three fast convergence methods are proposed for the simplified function by means of changing the step size of the classical Euler method in this manuscript. The results obtained are pretty good. First method is to correct the step size of two directions. Second method is to correct and encrypt two directions' step size. And the last method is to search unidirectional step size. On one hand, the feasibility of the three methods are proved based on the theoretical analysis. On the other hand, numerical results and comparison show that the advised three methods are effective to get the numerical solution with small population size, enhanced convergence speedup and improved precision.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130483390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Different from many previous studies which only applied one approach to analyze the multifractal properties of the stock market, this manuscript applies the partition function method (PF) and the multifractal detrended fluctuation analysis (MF-DFA) to investigate the multifractal properties of index distribution and fluctuations of the main stock markets in the world. After comparing the differences between the two multifractal approaches, it is found that the price distribution characteristic can be discovered by the partition function method, while the price fluctuation characteristic can be revealed via the MF-DFA. The empirical results show that index distribution and fluctuation multifractal properties of one stock market are different, so we can investigate the difference among the stock markets more comprehensively by applying the two approaches simultaneously.
{"title":"Comparison Study of Two Multifractal Approaches on Stock Markets","authors":"Zhang-xi Lin","doi":"10.1109/IWCFTA.2012.69","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.69","url":null,"abstract":"Different from many previous studies which only applied one approach to analyze the multifractal properties of the stock market, this manuscript applies the partition function method (PF) and the multifractal detrended fluctuation analysis (MF-DFA) to investigate the multifractal properties of index distribution and fluctuations of the main stock markets in the world. After comparing the differences between the two multifractal approaches, it is found that the price distribution characteristic can be discovered by the partition function method, while the price fluctuation characteristic can be revealed via the MF-DFA. The empirical results show that index distribution and fluctuation multifractal properties of one stock market are different, so we can investigate the difference among the stock markets more comprehensively by applying the two approaches simultaneously.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126967500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An SEIR model with varying total population size and continuous vaccination is proposed. The stability of the disease-free equilibrium is discussed, and the global stability of the disease-free equilibrium is discussed with the Lasalle's invariance principle. Using analytical methods, the existence and uniqueness of the positive equilibrium are obtained, and it's stability is also discussed by Routh-Hurwith criterion. Finally, numerical simulations are also included.
{"title":"Qualitative Analysis of an SEIR Model with Varying Total Population Size and Vaccination","authors":"Huitao Zhao, Yunxian Dai, Yiping Lin","doi":"10.1109/IWCFTA.2012.31","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.31","url":null,"abstract":"An SEIR model with varying total population size and continuous vaccination is proposed. The stability of the disease-free equilibrium is discussed, and the global stability of the disease-free equilibrium is discussed with the Lasalle's invariance principle. Using analytical methods, the existence and uniqueness of the positive equilibrium are obtained, and it's stability is also discussed by Routh-Hurwith criterion. Finally, numerical simulations are also included.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122426868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we will discuss the oscillation of solutions of higher-order nonlinear delay dynamic equations on time scales, which have the following form SnΔ (t, x) + p(t)f(x(τ(t))) = 0. We will establish some oscillation criteria for these dynamic equations. Our results improve some previously obtained ones.
{"title":"Oscillation of Solutions for Higher-order Nonlinear Delay Dynamic Equations on Time Scales","authors":"Zhanhuo Chen, T. Sun, Xin Wu","doi":"10.1109/IWCFTA.2012.28","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.28","url":null,"abstract":"In this paper, we will discuss the oscillation of solutions of higher-order nonlinear delay dynamic equations on time scales, which have the following form S<sub>n</sub><sup>Δ</sup> (t, x) + p(t)f(x(τ(t))) = 0. We will establish some oscillation criteria for these dynamic equations. Our results improve some previously obtained ones.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116463464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a new color image encryption algorithm based on the fractional-order hyper chaotic systems. First, two fractional-order hyper chaotic systems is applied to generate the chaotic sequences to scramble and diffuse the images. The system parameters, fractional order and initial conditions can be used as the secret keys. Second, we modify the RGB values of the plain-image pixels using six encryption matrices generating from two fractional-order hyper chaotic systems with a XOR operation two times. Third, the image pixel-position is further scrambled by a permutation matrix generating from a fractional-order hyper chaotic system. Finally, experimental results show the efficiency and high security of the proposed algorithm.
{"title":"A Color Image Encryption Algorithm Using the Fractional-order Hyperchaotic Systems","authors":"Xiangjun Wu","doi":"10.1109/IWCFTA.2012.50","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.50","url":null,"abstract":"This paper presents a new color image encryption algorithm based on the fractional-order hyper chaotic systems. First, two fractional-order hyper chaotic systems is applied to generate the chaotic sequences to scramble and diffuse the images. The system parameters, fractional order and initial conditions can be used as the secret keys. Second, we modify the RGB values of the plain-image pixels using six encryption matrices generating from two fractional-order hyper chaotic systems with a XOR operation two times. Third, the image pixel-position is further scrambled by a permutation matrix generating from a fractional-order hyper chaotic system. Finally, experimental results show the efficiency and high security of the proposed algorithm.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116986292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A method of encryption for embedding a meaningful gray image in the frequency domains of an audio signal is described. Chaotic sequence based on logistic map is adopted to improve the security of the proposed watermarking scheme by quantizing wavelet packet coefficients of audio samples. Simulations under various conditions are given to verify the effectiveness of the audio watermarking scheme. The results show the proposed scheme is secure, and the watermark is imperceptible and robust against audio signal processing attacks such as noising, low filtering, resampling and compressing.
{"title":"Chaotic Watermarking System for Audio Based on Wavelet Packet","authors":"Bo Zhou, Aiguo Shi","doi":"10.1109/IWCFTA.2012.45","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.45","url":null,"abstract":"A method of encryption for embedding a meaningful gray image in the frequency domains of an audio signal is described. Chaotic sequence based on logistic map is adopted to improve the security of the proposed watermarking scheme by quantizing wavelet packet coefficients of audio samples. Simulations under various conditions are given to verify the effectiveness of the audio watermarking scheme. The results show the proposed scheme is secure, and the watermark is imperceptible and robust against audio signal processing attacks such as noising, low filtering, resampling and compressing.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128494706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new three-dimensional continuous quadratic autonomous chaotic system with no equilibria is discussed. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, Analysis results show that this system has complex dynamics with some interesting characteristics.
{"title":"Complex Dynamics of a New Chaotic System without Equilibria","authors":"Zhouchao Wei","doi":"10.1109/IWCFTA.2012.27","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.27","url":null,"abstract":"A new three-dimensional continuous quadratic autonomous chaotic system with no equilibria is discussed. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, Analysis results show that this system has complex dynamics with some interesting characteristics.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"324 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116635888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article investigates the dynamical behavior in the fractional-order permanent magnet synchronous motor, firstly. Secondly, based on the Lyapunov equation stability theory of fractional-order systems, we scheme out corresponding controller, and realized the control of permanent magnet synchronous motor. And then Routh-Hurwitz conditions and numerical simulations are used to show the agreement between the theoretical and numerical results.
{"title":"Controlling of Fractional-order Permanent Magnet Synchronous Motor Based on Lyapunov Equation","authors":"Qiong Shen, Shaojuan Ma","doi":"10.1109/IWCFTA.2012.59","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.59","url":null,"abstract":"This article investigates the dynamical behavior in the fractional-order permanent magnet synchronous motor, firstly. Secondly, based on the Lyapunov equation stability theory of fractional-order systems, we scheme out corresponding controller, and realized the control of permanent magnet synchronous motor. And then Routh-Hurwitz conditions and numerical simulations are used to show the agreement between the theoretical and numerical results.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115225681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Aiping Jiang, Xiangxue Zhang, Luping Jiang, Jingquan Wang
This article describes a watermarking algorithm based on Fractional Brownian motion model in wavelet domain. In the watermark embedding process, we have taken advantage of the hearts matrix generated by the fractional brownian motion model, it successfully resolved the problem of watermarking visibility due to human eye' sensibility to low wavelet frequency. In order to enhance the security of the watermark, the algorithm is combined with one-dimensional chaotic scrambling encryption. In this article, we completed a large number of comparative experiments. The results showed the algorithm is very good to solve the contradiction between the transparency and robustness of the watermark. Also it has strong ability to resist conventional signal processing means such as geometric attacks, filtering attacks, noise attacks, and compression attacks. The proposed scheme demonstrates very good performance.
{"title":"A Wavelet Domain Watermarking Algorithm Based on Fractional Brownian Motion Model","authors":"Aiping Jiang, Xiangxue Zhang, Luping Jiang, Jingquan Wang","doi":"10.1109/IWCFTA.2012.68","DOIUrl":"https://doi.org/10.1109/IWCFTA.2012.68","url":null,"abstract":"This article describes a watermarking algorithm based on Fractional Brownian motion model in wavelet domain. In the watermark embedding process, we have taken advantage of the hearts matrix generated by the fractional brownian motion model, it successfully resolved the problem of watermarking visibility due to human eye' sensibility to low wavelet frequency. In order to enhance the security of the watermark, the algorithm is combined with one-dimensional chaotic scrambling encryption. In this article, we completed a large number of comparative experiments. The results showed the algorithm is very good to solve the contradiction between the transparency and robustness of the watermark. Also it has strong ability to resist conventional signal processing means such as geometric attacks, filtering attacks, noise attacks, and compression attacks. The proposed scheme demonstrates very good performance.","PeriodicalId":354870,"journal":{"name":"2012 Fifth International Workshop on Chaos-fractals Theories and Applications","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114086459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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